The Union of Soviet Socialist Republics (USSR), by launching a first satellite, Sputnik I, initiated the beginning of the space age, and space usage has gradually become an important area of research ever since. A global positioning system (GPS) was originated from a navigating system developed by the United States (US) Navy. The US Department of Defense (USDoD) continued the project and achieved a GPS by satellites.
The USDoD separated the GPS project into three stages including a research stage, a trial stage and a mature stage. The GPS was then opened to the public when the GPS entered the mature stage. Since the GPS is reliant on satellites, it is also referred to as the satellite positioning system (SPS). There are 32 GPS satellites with a period of 12 hours and a height of 20,000 kilometer (km).
In the process of receiving a satellite signal are many biases and errors. The biases have predetermined characteristics and can be represented by mathematical models, whereas the errors are randomly generated and need to be represented statistically—both the biases and errors have undesirable influence on the accuracy of the satellite positioning. One of the significant errors is a multipath effect. That is, except when receiving a satellite signal directly, i.e., a line-of-sight (LOS) signal, an antenna may also receive a satellite signal that has been reflected by objects in the environment, i.e., a multipath (MP) signal, in a way that the two signals reach the antenna at different timings. Therefore, when receiving an LOS signal and an MP signal that are superposed on each other, a receiver cannot estimate an accurate frequency because time difference and phase and/or frequency offset exist between the LOS signal and the MP signal.
Especially in a city with skyscrapers and narrow lanes, the multipath effect is quite serious, and thus poses a great challenge for the GPS that requires a high quality of measurement. It is to be noted that the prior art focused only to resolve time delay in the multipath effect. However, in a real environment, the multipath effect often includes frequency offset such that a range-rate is estimated incorrectly.
A two-path baseband signal includes the LOS signal and the MP signal, and the baseband signal r(t) can be represented as: r(t)=A1c(t−τ1)ej(2πf1t+θ1)+A2c(t−τ2)ej(2πf2t+θ2), where c(τ) is a coarse acquisition (C/A) code, A1, f1, τ1 and θ1 represent a signal strength, a frequency, a delay and a phase of the LOS signal respectively, and A2, f2, τ2 and θ2 represent a signal amplitude, a frequency, a delay and a phase of the MP signal respectively. The C/A code is a bit sequence that represents pseudorandom noise (PN code) where the C/A code strongly correlates to itself when two same C/A codes are exactly aligned. In GPS system, each satellite has its own C/A code which will not strongly correlate with other satellites' C/A code. Signals from different satellites are transmitted with their own C/A codes. Therefore, it is desired to correlate two received baseband signals r(t) in order to recover the original transmitted signal.
According to a coherent time T, a correlation is calculated by a time-and-carrier recovered correlation of the baseband signal in a time interval from (k−1)T to kT, and a correlation result is as follows:sk(τ,f)=(A1R(τ−τ1)sinc((f−f1)T))2+(A2R(τ−τ2)sinc((f−f2)T)2+A1A2 cos(2πfΔkT+θΔ)R(τ−τ1)R(τ−τ2)sinc((f−f1)T)sinc((f−f2)T)  (1),where fΔ=f1−f2, θΔ=θ1−θ2−πfΔT and R(τ) is an autocorrelation function of the C/A code.
In the prior art, multipath estimation neglects frequency dimension variations and it assumes the LOS signal and the MP signal have the same frequency so a simplified equation of Eq. (1) is obtained as follows:sk(τ)=(A1R(τ−τ1))2+(A2R(τ−τ2))2+2A1A2 cos(θΔ)R(τ−τ1)R(τ−τ2)  (2)
A1, τ1, A2, τ2 and θΔ are then estimated. As mentioned previously, the prior art cannot attend to situations where the LOS signal and the MP signal have a frequency difference.
FIG. 1 is a signal diagram of the LOS signal, the MP signal and a tracking (TRK) signal in a conventional positioning system. Ideally, a tracking signal frequency (fTRK) is equal to an LOS signal frequency (f1). However, since the prior art does not estimate a frequency influence caused by the MP signal, the recovered tracking signal frequency is shifted because of the MP signal frequency offset. A difference between the LOS signal frequency and the MP signal frequency (f2) can be up to 40 Hz, and a difference between the LOS signal frequency and the TRK signal frequency can be up to 30 Hz—such differences cause the positioning system huge errors in navigating speed and direction.
Hence, a frequency tracking method and apparatus applied to a positioning system is urgently needed to improve the MP effect estimation, so as to make the frequency tracking of the positioning system more accurate.